Explaining High Conjunction Fallacy Rates: The Probability Theory Plus Noise Account

The conjunction fallacy occurs when people judge the conjunctive probability P(A ∧ B) to be greater than a constituent probability P(A), contrary to the norms of probability theory. This fallacy is a reliable, consistent and systematic part of people's probability judgements, attested in many studies over at least 40 years. For some events, these fallacies occur very frequently in people's judgements (at rates of 80% or more), while for other events, the fallacies are very rare (occurring at rates of 10% or less). This wide range of fallacy rates presents a challenge for current theories of the conjunction fallacy. We show how this wide range of observed fallacy rates can be explained by a simple model where people reason according to probability theory but are subject to random noise in the reasoning process. Copyright © 2016 John Wiley & Sons, Ltd.     

新世纪20年国内测验信度研究

随着验证性因子分析模型的应用, 信度研究进入了崭新的发展阶段。新世纪前20年国内有关测验信度的研究有三条发展主线。一是基于验证性因子模型的信度发展, 包括同质性系数、合成信度、最大信度等; 二是数据类型的拓展, 包括两水平和追踪数据的信度; 三是信度用途的拓展, 如评分者信度、编码者信度等。对于通常的测验(题目之间的测量误差不相关), 如果α系数够高, 信度就够高; 否则使用合成信度。如果一个统计模型中所有变量的合成信度都很高(超过0.95), 使用显变量建模与使用潜变量建模的结果差别不大; 否则, 使用潜变量建模较好。     

3~5岁幼儿一位数大小比较的信息加工模式

主要探讨我国幼儿对数量大小比较的信息加工模式。实验1探讨幼儿对一位数大小比较的发展状况及其心理表征特点,被试为3岁、4岁与5岁幼儿各20人,要求被试对1-9两两进行大小比较,然后对不同年龄幼儿对比成绩进行比较与聚类分析。实验2进一步探讨幼儿对数字的语义编码情况及其与数的大小比较的关系,被试与实验1相同,要求被试对1-9每个数字作出大、中或小的编码,然后分析数字的语义编码成绩与大小比较成绩的关系。实验3采用因果设计,探讨幼儿关于数字的语义编码对他们关于数的大小判断的影响,被试为30名4岁幼儿,随机分成训练组与控制组,对训练组被试进行数字语义编码训练,然后比较两组被试大小比较的成绩。结果表明：(1)幼儿一位数大小比较直接受其对数的语义表征的影响;(2)随着年龄的增长,幼儿对数的表征逐步表现出离散聚类模式,相应地,对一位数大小比较的信息加工过程就表现为由无序的、随机的过程逐步发展成为层次编码比较的过程。     

SNARC (spatial–numerical association of response codes) meets SPARC (spatial–pitch association of response codes): Automaticity and interdependency in compatibility effects

Concepts, including the mental number line, or addressing pitch as high and low, suggest that the spatial–numerical and spatial–pitch association of response codes (SNARC and SPARC) effects are domain-specific and thus independent. Alternatively, there may be dependencies between these effects, because they share common automatic or controlled decision mechanisms. In two experiments, participants were presented with spoken numbers in different pitches; their numerical value, pitch, and response compatibility were varied systematically. This allowed us to study SNARC and SPARC effects in a factorial design (see also Fischer, Riello, Giordano, &; Rusconi, 2013 Fischer, M. H., Riello, M., Giordano, B. L., &; Rusconi, E. (2013). Singing numbers?…?in cognitive space--a dual-task study of the link between pitch, space, and numbers. Topics in Cognitive Science, 5(2), 354–366. Retrieved from http://doi.org/10.1111/tops.12017[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Participants judged the stimuli on numerical magnitude, pitch, or parity (odd–even). In all tasks, the SNARC and SPARC effects had superadditive interactions. These were interpreted as both effects sharing a common mechanism. The task variation probes the mechanism: In the magnitude judgement task, numerical magnitude was explicit, whereas pitch was implicit; in the pitch judgement task, it was vice versa. In the parity judgement task, both dimensions were implicit. Regardless of whether they were implicit or explicit, both SNARC and SPARC effects occurred in all tasks. We concluded that by not requiring focal attention the common mechanism operates automatically.     

学前儿童近似数量系统敏锐度与符号数学能力的关系

选取杭州市122名学前儿童(3~6岁)为被试,以点数比较任务及点数异同任务测量幼儿的近似数量系统敏锐度,以数数测验、基数测验、符号数字知识测验及简单计算来测量幼儿的符号数学能力,以此考察学前儿童近似数量系统敏锐度的发展及与符号数学能力的关系。结果发现:(1)随年龄增长,学前儿童的近似数量加工的敏锐度逐渐提高;(2)点数比较任务与点数异同任务均适合测量学前儿童近似数量系统敏锐度,但儿童完成点数比较任务的正确率要高于点数异同任务的正确率;(3)在抑制控制、短时记忆、工作记忆和言语测验成绩被控制后,根据点数比较任务计算的韦伯系数能显著预测学前儿童的基数和符号数字知识测验分数,总正确率能显著预测学前儿童的数数、基数、符号数字知识测验分数;(4)点数异同任务中只有点数不同试次下的正确率能显著预测学前儿童的符号数字知识测验分数。     

A bayesian alternative to least squares and equal weighting coefficients in regression

This paper details a Bayesian alternative to the use of least squares and equal weighting coefficients in regression. An equal weight prior distribution for the linear regression parameters is described with regard to the conditional normal regression model, and resulting posterior distributions for these parameters are detailed. Some interesting connections between this Bayesian procedure and several other methods for estimating optimal weighting coefficients are discussed. In addition, results are presented of a Monte Carlo investigation which compared the effectiveness of the Bayesian procedure relative to least squares, equal weight, ridge, and Bayesian exchangeability estimations.     

结构方程模型中调节效应的标准化估计

回归分析和结构方程分析中,标准化估计对解释模型和比较效应大小有重要作用。对于调节效应模型（或交互效应模型）,通常的标准化估计没有意义。虽然显变量的调节效应模型标准化估计问题已经解决,但潜变量的调节效应模型标准化估计问题复杂得多。本文先介绍回归分析中显变量调节效应模型的标准化估计,然后提出了一种通过参数的原始估计和通常标准化估计来计算潜变量调节效应模型的“标准化”估计的方法,得到的“标准化”估计是尺度不变的,说明可以用“标准化”估计来解释和比较主效应和调节效应     

Contextual effects on number-time interaction

Time perception has long been known to be affected by numerical representations. Recent studies further demonstrate that when participants estimate the duration of Arabic numbers, number magnitude, though task-irrelevant, biases duration judgment to produce underestimation for smaller numbers and overestimation for larger numbers. Such effects were found in the present study to be significantly reduced when a weight unit gram was suffixed to the numbers rendering the mental magnitude differences between different numbers less distinctive. The effects were enhanced when a different unit kilogram was suffixed to the numbers enlarging the perceived magnitude differences between different numbers. The results indicate that effects of number magnitude on duration estimation should not be attributed to the mathematical differences between numbers but to how the numbers are perceived to differ from each other in magnitude in specific contexts when they denote concrete items. The results also provide new evidence for the theoretical proposal of a common generalized magnitude system and indicate that the system must be extended to include other action-oriented magnitudes, such as weight.     

On the existence and uniqueness of maximum-likelihood estimates in the Rasch model

Necessary and sufficient conditions for the existence and uniqueness of a solution of the so-called unconditional (UML) and the conditional (CML) maximum-likelihood estimation equations in the dichotomous Rasch model are given. The basic critical condition is essentially the same for UML and CML estimation. For complete data matricesA, it is formulated both as a structural property ofA and in terms of the sufficient marginal sums. In case of incomplete data, the condition is equivalent to complete connectedness of a certain directed graph. It is shown how to apply the results in practical uses of the Rasch model.Paper read at the European Meeting of the Psychometric Society, Groningen, June 19–21, 1980.Part of the research reported herein was done while the author was staying at the Pulmologisches Zentrum der Stadt Wien; he is indebted to Professor Dr. F. Muhar and Dr. R. Mutschlechner for providing excellent working conditions.     

贝叶斯结构方程模型及其研究现状

在心理学研究中结构方程模型(Structural Equation Modeling, SEM)被广泛用于检验潜变量间的因果效应, 其估计方法有频率学方法(如, 极大似然估计)和贝叶斯方法两类。近年来由于贝叶斯统计的流行及其在结构方程建模中易于处理小样本、缺失数据及复杂模型等方面的优势, 贝叶斯结构方程模型发展迅速, 但其在国内心理学领域的应用不足。主要介绍了贝叶斯结构方程模型的方法基础和优良特性, 及几类常用的贝叶斯结构方程模型及其应用现状, 旨在为应用研究者介绍新的研究工具。